A note on a Broken-cycle Theorem for hypergraphs

TL;DR

This paper extends Whitney's Broken-cycle Theorem to hypergraphs by defining cycles in a way that maintains the theorem's original form, broadening its applicability beyond simple graphs.

Contribution

It introduces a new definition of cycles in hypergraphs that allows the Broken-cycle Theorem to be applied in this more general setting.

Findings

Extended the theorem to hypergraphs with a new cycle definition

Preserved the theorem's sum-over-edge-subsets formulation

Broadened the theorem's applicability to hypergraph chromatic polynomials

Abstract

Whitney's Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there.